Solve using cross-multiplication :

0.4x - 1.5y = 6.5

0.3x + 0.2y = 0.9

Simplifying first equation, we get :

⇒ 0.4x - 1.5y = 6.5

Multiplying both sides of the above equation by 10, we get :

⇒ 10(0.4x - 1.5y) = 10 × 6.5

⇒ 4x - 15y = 65

⇒ 4x - 15y - 65 = 0

Simplifying second equation, we get :

⇒ 0.3x + 0.2y = 0.9

⇒ 10(0.3x + 0.2y) = 0.9 × 10

⇒ 3x + 2y = 9

⇒ 3x + 2y - 9 = 0

So, the equations are

⇒ 4x - 15y - 65 = 0 ……..(1)

⇒ 3x + 2y - 9 = 0 ……..(2)

By cross-multiplication method, we get :

$\Rightarrow \dfrac{x}{(-15) \times (-9) - 2 \times (-65)} = \dfrac{y}{(-65) \times 3 - (-9) \times 4} = \dfrac{1}{4 \times 2 - 3 \times (-15)} \\[1em] \Rightarrow \dfrac{x}{135 + 130} = \dfrac{y}{-195 + 36} = \dfrac{1}{8 + 45} \\[1em] \Rightarrow \dfrac{x}{265} = \dfrac{y}{-159} = \dfrac{1}{53} \\[1em] \Rightarrow \dfrac{x}{265} = \dfrac{1}{53} \text{ and } \dfrac{y}{-159} = \dfrac{1}{53} \\[1em] \Rightarrow x = \dfrac{265}{53} \text{ and } y = \dfrac{-159}{53} \\[1em] \Rightarrow x = 5 \text{ and } y = -3.$

Hence, x = 5 and y = -3.